Legal claims defining the scope of protection, as filed with the USPTO.
1. A method for modeling a characteristic C that is distributed within a domain, said method comprising: storing a base equation in at least one computer-readable memory device, said base equation expressing the characteristic C as a function f of a variable V through use of N+1 parameters C 0 , C 1 , . . . , C N , said base equation being of a form C=f(C 0 , C 1 , . . . , C N , V), said N being at least 1, said parameters C 0 , C 1 , . . . , C N being subject to uncertainty; generating a probability density function (PDF) for describing a probability of occurrence of C 0 in accordance with said uncertainty; generating subsidiary equations expressing C 1 , . . . , C N in terms of C 0 ; and storing the PDF and the subsidiary equations in the at least one computer-readable memory device, wherein the base equation, the PDF, and the subsidiary equations are adapted to be accessed from the at least one memory device for usage in determining C.
2. The method of claim 1 , wherein C=C 0 if V=V 0 , and wherein generating the PDF comprises: providing test data of C=C 0 (k) at each node k of K nodes in a space such that V=V 0 at node k, said C 0 (k) being C 0 at node k, said K being at least 2, said k being an integer having values 1, 2, . . . , K; and generating said PDF from said test data.
3. The method of claim 1 , wherein generating the subsidiary equations comprise: providing test data of C(k) versus V at each node k of K nodes in a space, said C(k) being C at node k, said K being at least 2, said k being an integer having values 1, 2, . . . , K; fitting the function f to the test data at each node k of the K nodes to obtain C(k)=f(C 0 (k), C 1 (k), . . . , C N (k), V), said C 0 (k), C 1 (k), . . . , C N (k) respectively denoting C 0 , C 1 , . . . , C N at node k; and generating the subsidiary equations by utilizing C(k)=f(C 0 (k), C 1 (k), . . . , C N (k), V) at each node k of the K nodes.
4. The method of claim 1 , wherein the method further comprises: providing a value V′ of V; picking a random value C 0R of C 0 from the PDF; computing values C 1R , . . . , C NR of C 1 , . . . , C N , respectively, by substituting C 0R into the subsidiary equations; calculating a value of C by substituting C 0R , C 1R , . . . , C NR and V′ into the base equation; and outputting the calculated value of C to an output device.
5. The method of claim 1 , wherein the method further comprises determining a performance characteristic of a design, said design comprising I nodes in the domain, said I being at least 2, each node i of the I nodes having a value C(i) of the characteristic C, said i having values of 1, 2, . . . , I, said determining a performance characteristic comprising: randomly selecting a value of C(i) of C at each node i of the I nodes; determining the performance characteristic, including utilizing said randomly selected C( 1 ), C( 2 ), . . . , C(I); and outputting the determined performance characteristic to an output device.
6. The method of claim 5 , said randomly selecting a value of C(i) comprising: providing a value V(i) of V at node i; picking a random value C 0R of C 0 from the PDF; calculating corresponding values C 1R , . . . , C NR of C 1 , . . . , C N , respectively, by substituting C 0R into the subsidiary equations; and computing C(i) by substituting C 0R , C 1R , . . . , C NR and V(i) into the base equation.
7. The method of claim 1 , said PDF being a normal probability distribution.
8. The method of claim 1 , said subsidiary equations having a form of C x =g x (C x-1 ) for functions g x , said functions g x each being a linear of quadratic function of C x-1 , said x having values of 1, 2, . . . , N.
9. The method of claim 1 , said domain being a physical domain, said characteristic C being spatially distributed within said physical domain.
10. The method of claim 1 , said characteristic C being an electrical characteristic.
11. The method of claim 10 , said characteristic C denoting capacitance at a node of the domain, said V denoting a voltage applied to the node.
12. The method of claim 11 , said function f being a polynomial in V of order N, said N being at least 5.
13. The method of claim 12 , said N=2, said function f being C 0 /(1−V/V B ) m , said C 1 =V B , said C 2 =m.
14. A computer program product, comprising a computer usable medium having a computer readable program code embodied therein, said computer readable program code adapted to be executed on a processor for implementing a method for modeling a characteristic C that is distributed within a domain, said method comprising: storing a base equation in at least one computer-readable memory device, said base equation expressing the characteristic C as a function f of a variable V through use of N+1 parameters C 0 , C 1 , . . . , C N , said base equation being of a form C=f(C 0 , C 1 , . . . , C N , V), said N being at least 1, said parameters C 0 , C 1 , . . . , C N being subject to uncertainty; generating a probability density function (PDF) for describing a probability of occurrence of C 0 in accordance with said uncertainty; generating subsidiary equations expressing C 1 , . . . , C N in terms of C 0 ; and storing the PDF and the subsidiary equations in the at least one computer-readable memory device, wherein the base equation, the PDF, and the subsidiary equations are adapted to be accessed from the at least computer-readable one memory device for usage in determining C.
15. The computer program product of claim 14 , wherein the method further comprises: providing a value Y′ of V; picking a random value C 0R of C 0 from the PDF; computing values C 1R , . . . , C NR of C 1 , . . . , C N , respectively, by substituting C 0R into the subsidiary equations; calculating a value of C by substituting C 0R , C 1R , . . . , C NR and V′ into the base equation; and outputting the calculated value of C to an output device.
16. The computer program product of claim 14 , wherein the method further comprises determining a performance characteristic of a design, said design comprising I nodes in the domain, said I being at least 2, each node i of the I nodes having a value C(i) of the characteristic C, said i having values of 1, 2, . . . , I, said determining a perfonnance characteristic comprising: randomly selecting a value of C(i) of C at each node i of the I nodes; and determining the performance characteristic, including utilizing said randomly selected C( 1 ), C( 2 ), . . . , C(I); and outputting the determined performance characteristic to an output device.
17. The computer program product of claim 16 , said randomly selecting a value of C(i) comprising: providing a value V(i) of V at node i; picking a random value C 0R of C 0 from the PDF; calculating corresponding values C 1R , . . . , C NR of C 1 , . . . , C N , respectively, by substituting C 0R into the subsidiary equations; and computing C(i) by substituting C 0R , C 1 , . . . , C NR and V(i) into the base equation.
18. A computer readable medium comprising a model therein, said model configured to be used by a computer readable program code adapted to be executed on a processor for implementing a method that uses the model for modeling a characteristic C that is distributed within a domain, said model comprising: a base equation expressing a characteristic C as a function f of a variable V through use of N+1 parameters C 0 , C 1 , . . . , C N , said base equation being of a form C=f(C 0 , C 1 , . . . , C N , V), said N being at least 1, said parameters C 0 , C 1 , . . . , C N being subject to uncertainty, said characteristic C being distributed within a domain; a probability density function (PDF) for describing a probability of occurrence of C 0 in accordance with said uncertainty; and subsidiary equations expressing C 1 , . . . , C N in terms of C 0 , said program code comprising code for determining the characteristic C using said model.
19. The computer readable medium of claim 18 , wherein the program code comprises means for using the base equation, the PDF, and the subsidiary equations to calculate a value of C from input comprising a value V′ of V.
20. The computer readable medium of claim 18 , wherein the program code comprises means for using the base equation, the PDF, and the subsidiary equations to determine a performance characteristic of a design, said design comprising I nodes in the domain, said i being at least 2, each node i of the I nodes having a value C(i) of the characteristic C, said i having values of 1, 2, . . . , I.
21. The computer readable medium of claim 18 , said PDF being a normal probability distribution.
22. The computer readable medium of claim 18 , said subsidiary equations having a form of C x = g (C x-1 ) for functions g x , said functions g x each being a linear of quadratic function of C x-1 , said x having values of 1, 2, . . . , N.
23. The computer readable medium of claim 18 , said domain being a physical domain, said characteristic C being spatially distributed within said physical domain.
24. The computer readable medium of claim 23 , said characteristic C being an electrical characteristic.
25. The computer readable medium of claim 24 , said characteristic C denoting capacitance at a node of the domain, said V denoting a voltage applied to the node.
26. The computer readable medium of claim 25 , said function f being a polynomial in V of order N, said N being at least 5.
Unknown
May 8, 2007
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